University of California at Santa Barbara, Santa Barbara, California 93106, United States.
Langmuir. 2011 Jan 4;27(1):59-73. doi: 10.1021/la1023168. Epub 2010 Dec 3.
We consider the adhesive interaction energy between a pair of vesicles in the strong adhesion limit, in which bending forces play a negligible role in determining vesicle shape compared to forces due to membrane stretching. Although force−distance or energy−distance relationships characterizing adhesive interactions between fluid bilayers are routinely measured using the surface forces apparatus, the atomic force microscope, and the biomembrane force probe, the interacting bilayers in these methods are supported on surfaces (e.g., mica sheet) and cannot be deformed. However, it is known that, in a suspension, vesicles composed of the same bilayer can deform by stretching or bending, and can also undergo changes in volume. Adhesively interacting vesicles can thus form flat regions in the contact zone, which will result in an enhanced interaction energy as compared to rigid vesicles. The focus of this paper is to examine the magnitude of the interaction energy between adhesively interacting, deformed vesicles relative to free, undeformed vesicles as a function of the intervesicle separation. The modification of the intervesicle interaction energy due to vesicle deformability can be calculated knowing the undeformed radius of the vesicles, R0, the bending modulus, k(b), the area expansion modulus, k(a), and the adhesive minimum, W(P)(0), and separation, D(P)(0), in the energy of interaction between two flat bilayers, which can be obtained from the force−distance measurements made using the above supported-bilayer methods. For vesicles with constant volumes, we show that adhesive potentials between nondeforming bilayers such as |W(P)(0)| 5 × 10(−4) mJ/m2, which are ordinarily considered weak in the colloidal physics literature, can result in significantly deep (>10×) energy minima due to increase in vesicle area and flattening in the contact region. If the osmotic expulsion of water across the vesicles driven by the tense, stretched membrane in the presence of an osmotically active solute is also taken into account, the vesicles can undergo additional deformation (flattening), which further enhances the adhesive interaction between them. Finally, equilibration of ions and solutes due to the concentration differences created by the osmotic exchange of water can lead to further enhancement of the adhesion energy. Our result of the progressively increasing adhesive interaction energy between vesicles in the above regimes could explain why suspensions of very weakly attractive vesicles may undergo flocculation and eventual instability due to separation of vesicles from the suspending fluid by gravity. The possibility of such an instability is an extremely important issue for concentrated vesicle-based products and applications such as fabric softeners, hair therapeutics and drug delivery.
我们考虑了在强粘附极限下一对囊泡之间的粘附相互作用能，在这种极限下，与膜拉伸引起的力相比，弯曲力在确定囊泡形状方面的作用可以忽略不计。尽管使用表面力仪、原子力显微镜和生物膜力探针来测量表征流体双层之间粘附相互作用的力-距离或能量-距离关系，但这些方法中的相互作用双层都支撑在表面上（例如云母片），并且不能变形。然而，已知在悬浮液中，由相同双层组成的囊泡可以通过拉伸或弯曲而变形，并且还可以经历体积变化。因此，粘附相互作用的囊泡可以在接触区域形成平坦区域，这将导致与刚性囊泡相比，相互作用能增强。本文的重点是研究在两个囊泡之间的分离的函数下，与自由、未变形的囊泡相比，粘附相互作用的变形囊泡之间的相互作用能的大小。由于囊泡的可变形性而引起的囊泡相互作用能的改变可以通过以下方式计算：已知囊泡的未变形半径 R0、弯曲模量 k(b)、面积扩展模量 k(a)和两个平面双层之间的相互作用的粘附最小能 W(P)(0)和分离距离 D(P)(0)，这些参数可以从上述支持双层方法的力-距离测量中获得。对于具有恒定体积的囊泡，我们表明，胶体物理学文献中通常认为较弱的非变形双层之间的粘附势，如 |W(P)(0)|5×10(−4) mJ/m2，由于囊泡面积的增加和接触区域的变平，可能导致明显更深 (>10×)的能量最小值。如果也考虑到由于渗透压活性溶质存在而使紧张、拉伸的膜驱动的水在囊泡中的排出，则囊泡可以经历额外的变形（变平），这进一步增强了它们之间的粘附相互作用。最后，由于渗透压交换水引起的浓度差异导致的离子和溶质的平衡可以进一步增强粘附能。我们在上述条件下囊泡之间的粘附相互作用能逐渐增加的结果可以解释为什么非常弱吸引的囊泡悬浮液可能由于囊泡通过重力从悬浮液中分离而发生絮凝聚并最终不稳定。这种不稳定性的可能性对于基于囊泡的浓缩产品和应用（例如织物柔软剂、头发治疗剂和药物递送）来说是一个极其重要的问题。
